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OverviewThe authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They then show that the introduction of an ``edge'', via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized ``edge states''. These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect. Full Product DetailsAuthor: C.F. Fefferman , J.P. Lee-Thorp , M.I. WeinsteinPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.200kg ISBN: 9781470423230ISBN 10: 1470423235 Pages: 118 Publication Date: 30 May 2017 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsIntroduction and outline Floquet-Bloch and Fourier analysis Dirac points of 1D periodic structures Domain wall modulated periodic Hamiltonian and formal derivation of topologically protected bound states Main Theorem--Bifurcation of topologically protected states Proof of the Main Theorem Appendix A. A variant of Poisson summation Appendix B. 1D Dirac points and Floquet-Bloch eigenfunctions Appendix C. Dirac points for small amplitude potentials Appendix D. Genericity of Dirac points - 1D and 2D cases Appendix E. Degeneracy lifting at Quasi-momentum zero Appendix F. Gap opening due to breaking of inversion symmetry Appendix G. Bounds on leading order terms in multiple scale expansion Appendix H. Derivation of key bounds and limiting relations in the Lyapunov-Schmidt reduction ReferencesReviewsAuthor InformationC. F. Fefferman, Princeton University, New Jersey. J. P. Lee-Thorp, Columbia University, New York, NY. M. I. Weinstein, Columbia University, New York, NY. Tab Content 6Author Website:Countries AvailableAll regions |
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